We notice that this simply corresponds to an \(\ell _p\) -sketch of the vector \(z \in ^n\) , which is given by letting each \(z_i = \lambda ^{1/p} \circ (x_i - y)\) , so that the \(\ell _p\) -sketch of [1]} would accomplish this task. Since the algorithm receives \(\) , \((\lambda ^{1/p} \circ x) + \mathrm {err}\cdot \chi \)  and \(y \in \) , the algorithm may compute \((\lambda ^{1/p} \circ y \cdot )\) , where \(\in ^n\)  is an all-1's vector, and evaluate the sketch
\( (\lambda ^{1/p} \circ x) + \mathrm {err}\cdot - (\lambda ^{1/p} \circ y \cdot ) = (\lambda ^{1/p} \circ (x - y\cdot )) + \mathrm {err}\cdot \) 
